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Fitting \(\alpha \) \(\beta \)-crystalline structure onto electron microscopy based on SO(3) rotation group theory

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Abstract

Based on SO(3) rotation group theory, a method is presented to fit \(\alpha \) \(\beta \)-crystalline structure on to its corresponding electron microscopy (EM) model for the further diagnosis of crystalline disease. Taken EM model as a kind of \(\alpha \) \(\beta \)-crystalline model rotation deformation, image processing techniques are firstly preformed and then mesh generation adopted on the obtained EM, depending upon its molecular features. Secondly, rigid-body fitting is performed to fit \(\alpha \) \(\beta \)-crystalline Protein Data Bank (PDB) data onto its EM by using SO(3) rotation group theory. Among the fitting process, FFT is adopted to tackle the problems of large data and high computation. The PDB file is obtained from NCBI and EM file obtained from EMBL-EBI. All of the tools are developed by CVC, ICES, the University of Texas at Austin. The experimental results show that it’s a precise and efficient method of fitting \(\alpha \) \(\beta \)-crystalline PDB crystal structure onto its EM model.

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Acknowledgments

This work is partially supported by the Leading Academic Discipline Project of Communication and Information System of Shanghai Second Polytechnic University Grant (No. XXKZD1302) and Study of the operational mechanism and its optimization of resource management in surgical operations of School of Medicine, Shanghai General Hospital, Shanghai Jiaotong University (No. 71371120).

Conflict of interest

The authors declare that they have no conflict of interest.

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Authors and Affiliations

  1. School of Engineering, Shanghai Second Polytechnic University, Shanghai, 201209, China

    Beibei Li

  2. Center for Computational Visualization, The Institute of Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX, 78712, USA

    Beibei Li & Zhihong Zhao

  3. School of Energy and Electrical Engineering, Nanjing Institute of Industry Technology, Nanjing, 210023, China

    Zhihong Zhao

  4. School of Software Technology, Dalian University of Technology, Dalian, 116024, China

    Xuan Shen

  5. School of Public Administration, Southwest Jiaotong University, Chengdu, 61003, China

    Cendi Xue

  6. Shanghai General Hospital, School of Medicine, Shanghai Jiaotong University, Shanghai, 200080, China

    Liwei Zhong

  7. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Liwei Zhong

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  1. Beibei Li
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  2. Zhihong Zhao
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  3. Xuan Shen
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  4. Cendi Xue
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  5. Liwei Zhong
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Correspondence to Liwei Zhong.

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Li, B., Zhao, Z., Shen, X. et al. Fitting \(\alpha \) \(\beta \)-crystalline structure onto electron microscopy based on SO(3) rotation group theory. J Comb Optim 30, 906–919 (2015). https://doi.org/10.1007/s10878-015-9858-x

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  • DOI: https://doi.org/10.1007/s10878-015-9858-x

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